To understand the origin of the nodal gap structure realized in BaFe${}_2$(As,P)${}_2$, we study the three-dimensional gap structure based on the three-dimensional ten-orbital Hubbard model with quadrupole interaction. In this model, strong spin and orbital fluctuations develop when the random-phase approximation is used. By solving the Eliashberg gap equation, we obtain the fully gapped $s$-wave state with (without) sign reversal between holelike and electronlike Fermi surfaces due to strong spin (orbital) fluctuations, the so-called $s_{\pm }$-wave ($s_{++}$-wave) state. When both spin and orbital fluctuations develop strongly, which will be realized near the orthorhombic phase, we obtain a nodal $s$-wave state in the crossover region between the $s_{++}$-wave and $s_{\pm }$-wave states. The nodal $s$-wave state obtained possesses loop-shaped nodes on electronlike Fermi surfaces, due to the competition between attractive and repulsive interactions in $\mathit{k}$ space. In contrast, the superconducting gaps on the holelike Fermi surfaces are fully gapped due to orbital fluctuations. The present study explains the main characteristics of the anisotropic gap structure in BaFe${}_2$(As,P)${}_2$ observed experimentally.

• Received 22 March 2013

DOI:https://doi.org/10.1103/PhysRevB.88.045115